$S_y^2 = \frac{1}{N-1}\sum_{k \in U}(y_k - \bar{Y})^2$ is equal to $\frac{1}{2N(N-1)}\sum_{k \in U} \sum_{l \in U \\ l \neq k}(y_k - y_l)^2$
I have to proof this for an exercise but am stuck at the very beginning.
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1The meaning of this equation is explained (without any mathematical demonstration) at https://stats.stackexchange.com/questions/18058/how-would-you-explain-covariance-to-someone-who-understands-only-the-mean/18200?s=1|0.0000#18200. Could you explain what it means to be "stuck at the very beginning"? Is this a matter of understanding what the symbols mean? If not, then what? – whuber Jan 26 '18 at 14:00
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@whuber My guess is that Florian has no idea how to start on the proof. As you know, our self-study question policy is to show what you've done so far, but if you have no idea how to start, then what? But maybe Florian will answer – Peter Flom Jan 26 '18 at 14:05
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@Peter If one absolutely has no idea of how to start on a proof of a mathematical equation, then *a fortiori* the question is not statistical and so would be off topic here. – whuber Jan 26 '18 at 14:29
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Let me clarify, and sorry for being unspecific: I understand the symbols, I replaced $\bar{Y}$ with $\frac{1}{N}\sum_{k \in U}y_k$ and I have suspected that it might be about covariance. But I could not get further. I fail to see the relation between the two expressions. – Florian Jan 26 '18 at 15:16
